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A method for demand-accurate one-dimensional cutting problems with pattern reduction.

Haihua Xiao1,2, Qiaokang Liang1,2, Dan Zhang3

  • 1College of Electrical and Information Engineering, Hunan University, Changsha 410082, China.

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|May 10, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new mathematical model to solve the one-dimensional cutting stock problem (1D-CSP). The method effectively reduces the number of cutting patterns, achieving significant reductions in real-world applications.

Keywords:
column generationcuttingcutting patterncutting stockoptimization algorithms

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Area of Science:

  • Operations Research
  • Industrial Engineering
  • Applied Mathematics

Background:

  • The one-dimensional cutting stock problem (1D-CSP) traditionally focuses on minimizing material costs.
  • Reducing the number of distinct cutting patterns is a crucial auxiliary objective in practical 1D-CSP scenarios.
  • Classical integer 1D-CSP requires precise satisfaction of item demands, prohibiting overproduction or underproduction.

Purpose of the Study:

  • To propose a novel mathematical model and method for the integer one-dimensional cutting stock problem (IDCSP).
  • To address the auxiliary objective of minimizing the variety of cutting patterns used.
  • To ensure exact demand satisfaction without allowing for surplus material.

Main Methods:

  • Development of a new mathematical model for the IDCSP.
  • Implementation of a variable-to-constant solution approach.
  • Integration and comparison with two established representative methods.

Main Results:

  • The proposed methodology demonstrates effectiveness in reducing the number of cutting patterns.
  • Experiments on benchmark and real-world instances validate the approach.
  • Significant pattern reduction (31.93% to 37.6%) achieved for real-life instances compared to existing methods and commercial software.

Conclusions:

  • The novel variable-to-constant method offers a superior solution for the IDCSP, particularly in reducing pattern variety.
  • The approach provides practical benefits for industries dealing with cutting stock optimization.
  • This research contributes an effective tool for enhancing efficiency and reducing waste in manufacturing processes.